Cognitive Psychology - Problem-Solving Vocabulary

Contact Information

• Email: cwalsh@plymouth.ac.uk
• Office: PSQ A211
• Office Hours: Tuesdays 1-2 pm, Thursdays 1-2 pm

Topics

• Problem-Solving
• Types of Problems
• Approaches to Problem-Solving
• Expertise and problem-solving

What is a Problem?

• Start State: Current situation
• Goal State: Desired situation
• A problem exists when the path from the start state to the goal state is unclear (subjective).

Cheap Necklace Problem

• Scenario: Four chains, each with three links, need to be combined into one chain.
• Cost: 2 cents to open a link, 3 cents to close a link.
• Objective: Determine the least costly method.

Types of Problems

• Well-defined Problems: All aspects (initial state, goal state, possible moves) are clearly defined.
• Ill-defined Problems: Start state, end state, or possible strategies are unknown; common in everyday situations.
• Knowledge-lean Problems: Do not require specific knowledge; often puzzles. For example:
  • Viral Math Puzzle
    • Equation 1: \Box + \Box + \Box = 23
    • Equation 2: \Box + \Box + \triangle = 45
    • Equation 3: \triangle + \triangle + \bigcirc = 23
    • Equation 4: \bigcirc + \Box + \Box = 10
    • Solve: \Box + \triangle + \bigcirc = ??
• Knowledge-rich Problems: Require specific knowledge.

Theories of Problem-Solving

• Behaviourist Approach
• Gestalt Approach
  • Problem Restructuring
• Information Processing
• Analogical Problem-Solving

Behaviourist Approach

• Trial and Error Learning
  • Thorndike's (1898) cat experiment.
  • Involves unsystematic behaviour.
  • Requires no prior knowledge.
  • Slow process.
  • Not effective for all problems.
  • Can be risky.

Gestalt Approach

• Problem-solving involves insight.
• "Aha" Moment
• Sudden realization or understanding.
• Problem restructuring
  • Koehler's (1925) Monkey Experiment.
    • Problem is solved after an incubation period.

Functional Fixedness

• Duncker's (1945) Candle Problem:
  • Task: Fix and light a candle on the wall so wax doesn't drip on the table.
• Maier (1931) Two-string problem:
  • Goal: Tie two hanging strings together.
  • Solution often facilitated by unconscious hints.

Neuroscience and Insight

• Bowden et al. (2005):
  • Activation in the Right anterior superior temporal gyrus.
  • FMRI: Showed insight relative to non-insight solutions.
  • EEG: Recorded activity prior to insight.

Incubation

• Many studies show effects, though fairly small, usually in creative problems with multiple solutions (Sio & Ormerod, 2009).
• May occur because people forget misleading or irrelevant information (Penaloz & Calvillo, 2012).

Evaluation of Gestalt Approach

• Recognizes the role of insight.
• Mechanisms underlying insight are not specified.

Representational Change Theory (Ohlsson, 1992)

• Aims to explain the processes underlying insight.
• Construct a problem representation.
• Retrieve operators (moves/actions) from memory by spreading activation from the problem representation.
• Impasses occur when the problem representation does not cue the right operators.
• Impasses are broken by restructuring the problem representation.
• Once an impasse is broken a full or partial insight may occur.

Changing Problem Representation

• Changing the representation of the problem.
• Relaxing the constraints on what moves are allowed.

Examples of Representational Change

• Changing the representation of a problem
  • The new board has 62 squares. Can you cover the whole board with 31 dominos?
• Relaxing the Constraints
  • Knoblich, Ohlsson, Haider & Rhenius (1999) In each case, move one matchstick so that the equation is correct.

Evaluation of Representational Change Theory

• Explains some mechanisms underlying insight.
• Doesn’t explain what leads to representational change or why incubation helps.

Information Processing Approach

• Allen Newell and Herb Simon (1972)
• Computational modelling approach: General Problem Solver.
• Most problems don’t require insight, focus instead on well-defined knowledge-lean problems.

General Problem Solver (Newell & Simon, 1972)

• Problem Space: all possible states of a problem (e.g., all chess positions).
• Initial State: starting position.
• Goal State: final position (e.g., check mate).
• Operators: Allowed moves or actions (e.g., chess moves).
• Problem-solving is a search through the problem space.
• We don’t have the working memory capacity to think of all possible moves; use general-purpose heuristics instead.
• Objective measure of optimal performance; can test whether people make moves consistent with the heuristics.

Heuristics

• Forward search: Start from the initial state and move towards the goal.
• Backward search: Start from the goal state and work backward to the initial state.
• Avoid loops: Prefer new solutions; if a solution doesn't work, try something different.
• Hill-Climbing:
  • Choose a move that brings you closer to the goal.
  • Can lead to problems if the next step does not bring us closer to the goal, e.g., intermediate peaks or plateaus.

Missionaries and Cannibals Problem

• Goal: Move 3 missionaries and 3 cannibals across the river.
• Constraints:
  • Only 2 fit in the boat.
  • Cannot be more cannibals than missionaries in any place.

Means-End Analysis

• Strategies for choosing the best move.
• Create a sub-goal.
• Choose a move that will bring you to the sub-goal.

Tower of Hanoi

• Aim to move all of the disc to the last peg.
• Only one disc can be moved at a time.
• You can’t put a larger disc on a smaller one.

Evaluation of Information Processing Approach

• Works well for well-defined problems.
• Good objective measures of how well people perform.
• Led to well-specified computer models.
• Many everyday problems are ill-defined.
• Doesn’t work for Insight Problems.

Analogical Problem-Solving

• How do we learn from past problems?
  • Negative Transfer – Functional fixedness.
  • Positive Transfer
    • Near transfer to a similar context.
    • Far transfer to a different context.
• Learning from analogy involves identifying surface features and structural features.

General Problem (Gick & Holyoak, 1980)

• A general was trying to destroy a fortress which was situated at the centre of a country with roads leading to it, by using his army. He needed to use his army as a complete group in order to destroy the fortress. However, he could not march his army down a road to the fortress because the roads were mined to explode when large groups of men passed over them.

Surgeon Problem

• Suppose you are a doctor with a patient who has a malignant tumour in his stomach. It is impossible to operate on the patient; but unless the tumour is destroyed the patient will die. There is a kind of ray that can be used to destroy the tumour. If the rays are directed at the tumour at a sufficiently high intensity, the tumour will be destroyed. Unfortunately, at this intensity the healthy tissue that the rays pass through on the way to the tumour will also be destroyed. At lower intensities the rays are harmless to the healthy tissue but they will not affect the tumour either. What type of procedure might be used to destroy the tumour with the rays, and at the same time avoid destroying the healthy tissue?

Steps in Analogical Problem Solving (Gick & Holyoak, 1980)

• Recognize that the two problems share a similar problem.
• Mapping (Army -> Rays, Fortress -> Tumour, Mines -> Healthy tissue).
• Apply the solution from one to the other.

Surgeon Problem (Keane, 1987)

• A surgeon was trying to destroy a cancer which was situated in the central region of a patient's brain, by using a type of ray. He needed to use these rays at a high intensity in order to destroy the cancerous tissue. However, at such an intensity the healthy brain tissue will also be destroyed. After considerable thought, he knew just what to do. He divided the rays up into batches of low-intensity rays, and by sending them, simultaneously, from a number of different directions, they converged on the cancer, making up a sufficiently high intensity to destroy it.

Analogical Mapping (Keane, 1987)

• Retrieval & Mapping
  • Solving the Radiation Problem depends on Fortress / Surgeon relations.

Evaluation of Analogical Problem-Solving

• Retrieving analogies is hard unless the problems share similar surface features.
• In real life, this may be even more difficult because the time and context may be more distant than in lab studies.
• Individual differences are not well understood.

Expertise

• Focus on problems that depend on extensive knowledge and learning.

Chess Expertise

• Adriaan De Groot compared experts and grandmasters, presented chess problems, and used 'Think-aloud' protocols.
• De Groot (1965; 1966) Comparison of 5 Grand Masters and 5 Experts
  • Number of first moves considered: Grand Masters (4.2), Experts (3)
  • Maximum depth of search: Grand Masters (6.8), Experts (6.6)
  • Time to choose move: Grand Masters (9.6 mins), Experts (12.9 mins)
  • Move Rating: Grand Masters (8.2), Experts (5.2)
• Chess expertise is not due to superior search skills.
• De Groot (1965)
  • 5-second presentation of board positions:
    • Recall: Chess masters (91%), Experts (43%).
    • Both poor at remembering random positions.

Medical Experts

• Melo et al. (2012) Medical Experts are very fast at detecting tumours (~1 sec).
• Activates same brain areas as object recognition.
• Experts use fast and automatic processes which develop with practice.

General Characteristics of Expertise

• Many years of practice are required.
• Have a lot of knowledge which they can access quickly.
• Use more automatic processes.

Summary

• Behaviourist approach: Trial and Error learning.
• Gestalt psychologist & Representation Theory: Insight Problems.
• Information Processing Approach: Well-defined Problems.
• Analogical Problem-Solving: Learning from Experience.
• Expertise: Knowledge-rich problems.